Brute-force the relations before trusting an 'infeasible' linear-algebra certificate search

When searching for an algebraic certificate (here, quasi-polynomial weights F, K so that a convolution sum over ax+by=n becomes divisor sums), an 'inconsistent' rank result is only meaningful if every relation in the system is correct. Cheap check: draw random functions of the ansatz type (random integer coefficients per residue class mod 4, times monomials), then compare both sides of each relation by brute force over the full solution set for a few n (12, 30, 37). Do this in plain Python; it takes seconds. Also sanity-run the solver on a case known to be feasible, at the SAME polynomial degree. The operators preserve total degree, so a degree-0 test case run with degree-1 unknowns is reported inconsistent and looks like a solver bug when it is not.